Although other parts may be used, chicken breasts work best. They cook quickly and evenly; have little fat and no veins; no meat is left clinging to the bone; and the long grain of the white meat makes it ideal for shredding.

Put chicken breasts, vegetables and seasonings into a large pot, and cover with 4 cups of cold water. Bring to a boil, then reduce the heat and simmer for 15 minutes, until the chicken is just cooked. Transfer the chicken and stock to a large bowl and let it all cool gradually. Once cool, remove the chicken from the bowl and rinse it off, strain and reserve all of the stock, reserve 1/2 cup of the cooked onions, and discard the rest of the vegetables. By hand, shred the chicken along the grain of the meat into thin strips, 1" to 2" long.

Clean out the pot, put the stock back into it and simmer it down to 2 cups. Remove crusts from the bread, then use a blender or food processor to reduce it to 1 cup of crumbs. Set aside the crumbs and put the walnuts into the blender or food processor; grind them finely; then add the garlic, reserved onion, and bread crumbs, and blend them all together. A little at a time, blend in up to 2 cups of stock, until you have a smooth, thick puree. Add salt, pepper, and a pinch of cayenne or hot paprika to taste. If the puree is too thick, add a little milk or water; if too thin, simmer over low heat until it thickens again.

In a small pan combine oil and paprika over very low heat until the oil begins to redden. Turn off the heat, let the oil cool, then strain, reserving the oil and discarding the paprika.

Mix up the chicken with half of the sauce, then put it into a serving platter. Spread the rest of the sauce over the chicken like frosting on a cake. Drizzle with paprika oil. Serve chilled or at room temperature.